Dyn's conjecture on the regularity of generalized Daubechies wavelets

Let $n\ge 2$ and let $\Lambda_n=\{\lambda_0,\ldots,\lambda_{n-1}\}$ be an arbitrary set of real numbers. Let $\psi^{\Lambda_n}$ be the generalized Daubechies wavelet associated with $\Lambda_n$, and let $\varphi_n$ be the classical stationary $n$th Daubechies refinable function. Write $\alpha_{\psi^{\Lambda_n}}$ and $\alpha_{\varphi_n}$ for their Hölder exponents. Dyn's conjecture. The Hölder regularity of every generalized Daubechies type wavelet is equal to the Hölder regularity of the corresponding classical Daubechies wavelet, equivalently

$$\alpha_{\psi^{\Lambda_n}}=\alpha_{\varphi_n}.$$

The generalized wavelets arise from non-stationary subdivision schemes reproducing exponential polynomials with spectrum $\Lambda_n$, while the classical wavelets arise from the limiting stationary masks. The paper proves this conjecture using its regularity theorem under the stated convergence and approximate sum-rule assumptions.